Which is the constructive interference formula for diffraction grating problems?

dsin =
dcos =
dcos = n
dsin = n

The formula for the brighter patches resulting from constructive interference and darker patches resulting from destructive interference in a diffraction grating is:

dsin(θ) = nλ

Here, d is the spacing between the grating, θ is the angle of light, n is the fringe order and λ is the wavelength. N has integer values only.

Destructive interference occurs between the fringes, so the formula for destructive interference becomes:

dsin(θ) = (n+1/2)λ, where n is again an integer.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this